Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n1, num, count;
  cin >> n1;
  int n = n1 * 2;
  int inum = sqrt(n);
  bool is = false;
  for (int i = 1; i <= inum; i++) {
    num = n - (i * i + i);
    int l = 0, r = inum, m;
    if (i == 30) {
      int b;
      int c;
      int s;
    }
    while (l <= r) {
      m = (l + r) / 2;
      if (m * m + m > num) {
        r = m - 1;
      } else if (m * m + m < num) {
        l = m + 1;
      } else {
        is = true;
        count = m;
        goto loop;
      }
    }
  }
loop:
  if (is && count != 0) {
    cout << "YES" << endl;
  } else {
    cout << "NO" << endl;
  }
  return 0;
}